I can't cite any hard empirical evidence, and I wonder if the people who profit from selling us more controllers would be inclined to sponsor such an evaluation. However . . .

I was chatting with my local rep about upgrades . . . we found out the version of the controllers we've been running are obsolete and several revisions behind. After ten years none of the controllers shows less than 60% free time. In contrast, my neighbor who works in a plant of similar complexity is already taxing the current generation of controllers (albeit the older form factor e.g. "M" versus "S").

The only difference is that our plant has 80% of loops solved in field devices. While my neighbor has a little FF, most of the loops (especially control) are 4-20 mA / HART.

So perhaps there's some evidence that solving control in the field saves some controller processing time. On the other hand, if you implement a lot of the "Human Centered Design" bells and whistles, some of the savings could become a wash.